Okay so, to clear up some of the points here.
1) Final Fantasy XIII and Versus XIII are two seperate gamesthat do nottake place within the same world. According to what Squeenix has revealed the games are part of the same compilation because they all center around a common mythos. Versus XIII does not take place in FFXIII's Pulse or Cocoon world just as much as FFXIII doesn't take place in whatever world Versus is in. However, both game's universes and stories center around something about crystals and how they shape life and the world around them. Hence, Fabula Nova Crystalis--Latin defined as The New tale of the crystal.
2) The way in which the two games play is different. FFXIII is a continuation or evolution of the classic FF gameplay that we are used to. (Namely the ATB system has been revamped to allow the player to perform multiple actions in one character turn.) On the opposite side VSXIII, while still kept pretty well under wraps at the moment, has been revealed to be an Action RPG very much like Kingdom hearts. In fact that brings me to my third point...
3) The Development teams behind the two games are quite a mixed bag of extremely talented workers from some of the most highly regarded FF titles of the past. For instance the Director of FFXIII was the Directer for FFs VII, VIII, X, and X-2. The Majority of that team worked on those previous titles. On the VSXIII side (pun intended), The Director is Tetsuya Nomura whom you may recall as SE's very talented character designer. The team that is making it worked on Kingdom hearts and FFVII:AC. Nomura himself said that the gameplay is going to be an evolution of the kingdom hearts style.
Another difference between the two titles is that FFXIII is supposed to represent the theme of Light and life while adversely, VSXIII represents the theme of Darkness and Death. This is evidenced by the the glaringly different art style of the two. FFXIII is full of vibrant bright colors while Versus is full of midnight-blues and Black. You can also tell this by the name of the main character of Versus: Noctis. It is a Latin word that means "of the night". (and by the way, Versus in latin means "a change in direction".) and I'm just gonna take a wild guess and say that Lightings real name is going to be something that means Day, Sun, or life. who knows? but it wouldn't be surprising.
and a side note, both game's gameplay styles are aimed at trying to imitate to the actions sequences seen in the Advent Children movie. Even though the two are different types of RPGs.
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